Identification

Identifying a ring of conflict is easy. Just put on the (ideally noncursed) ring and see if any peacefuls attack you, or if monsters attack each other. A common YASD is to BUC test a ring as noncursed in a temple and immediately wear it; if it's conflict, chances are good the priest will obliterate you.

Dropping a ring of conflict into a sink produces the message, "You hear loud noises coming from the drain."

A ring of conflict can be eaten for a chance of obtaining conflict as an intrinsic. Note that intrinsic conflict has the same nutrition cost as extrinsic conflict, minus the ring hunger.

Strategy

The main use of rings of conflict is to get enemies to attack and kill each other.

First, make sure your ring is non-cursed.
Also, stock up on food or have enough nutrition so you don't starve.
Next, stand within 8 squares of the monsters you want dead, and put on the ring.
Note that monsters will only randomly attack things that are adjacent to themselves, but use ranged attacks only on you.
So you will want to stay at least one square away from all monsters, and keep monsters (if possible) close to each other.
Thus, if the monsters ever get away from each other, or close to you, take off the ring!

This strategy can be helped if you have a physical way of keeping monsters confined to a small area:

Luring monsters into small rooms or shops, and closing or locking the door(s)